Dynamical Models of Interrelation in a Class of Artificial Networks

Felix Sadyrbaev; Svetlana Atslēga; Eduard Brokan

doi:10.1007/978-3-030-56323-3_18

Dynamical Models of Interrelation in a Class of Artificial Networks

Felix Sadyrbaev^*
, Svetlana Atslēga
, Eduard Brokan

^*Corresponding author for this work

University of Latvia

University of Latvia
Daugavpils University

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › Research › peer-review

3 Citations (Scopus)

Abstract

The system of ordinary differential equations that models a type of artificial networks is considered. The system consists of a sigmoidal function that depends on linear combinations of the arguments minus the linear part. The linear combinations of the arguments are described by the regulatory matrix W. For the three-dimensional cases, several types of matrices W are considered and the behavior of solutions of the system is analyzed. The attractive sets are constructed for most cases. The illustrative examples are provided. The list of references consists of 12 items.

Original language	English
Title of host publication	Differential and Difference Equations with Applications, ICDDEA 2019
Editors	Sandra Pinelas, Sandra Pinelas, John R. Graef, Stefan Hilger, Peter Kloeden, Christos Schinas
Place of Publication	Cham
Publisher	Springer Nature Switzerland
Pages	225-237
Number of pages	13
Volume	333
ISBN (Print)	9783030563226
DOIs	https://doi.org/10.1007/978-3-030-56323-3_18
Publication status	Published - 2020

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	333
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Keywords

Artificial networks
Attractors
Critical points
Dynamical systems
Gene regulatory networks

Access to Document

10.1007/978-3-030-56323-3_18

Cite this

Sadyrbaev, F., Atslēga, S., & Brokan, E. (2020). Dynamical Models of Interrelation in a Class of Artificial Networks. In S. Pinelas, S. Pinelas, J. R. Graef, S. Hilger, P. Kloeden, & C. Schinas (Eds.), Differential and Difference Equations with Applications, ICDDEA 2019 (Vol. 333, pp. 225-237). (Springer Proceedings in Mathematics and Statistics; Vol. 333). Springer Nature Switzerland. https://doi.org/10.1007/978-3-030-56323-3_18

Sadyrbaev, Felix ; Atslēga, Svetlana ; Brokan, Eduard. / Dynamical Models of Interrelation in a Class of Artificial Networks. Differential and Difference Equations with Applications, ICDDEA 2019. editor / Sandra Pinelas ; Sandra Pinelas ; John R. Graef ; Stefan Hilger ; Peter Kloeden ; Christos Schinas. Vol. 333 Cham : Springer Nature Switzerland, 2020. pp. 225-237 (Springer Proceedings in Mathematics and Statistics).

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title = "Dynamical Models of Interrelation in a Class of Artificial Networks",

abstract = "The system of ordinary differential equations that models a type of artificial networks is considered. The system consists of a sigmoidal function that depends on linear combinations of the arguments minus the linear part. The linear combinations of the arguments are described by the regulatory matrix W. For the three-dimensional cases, several types of matrices W are considered and the behavior of solutions of the system is analyzed. The attractive sets are constructed for most cases. The illustrative examples are provided. The list of references consists of 12 items.",

keywords = "Artificial networks, Attractors, Critical points, Dynamical systems, Gene regulatory networks",

author = "Felix Sadyrbaev and Svetlana Atslēga and Eduard Brokan",

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year = "2020",

doi = "10.1007/978-3-030-56323-3\_18",

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Sadyrbaev, F, Atslēga, S & Brokan, E 2020, Dynamical Models of Interrelation in a Class of Artificial Networks. in S Pinelas, S Pinelas, JR Graef, S Hilger, P Kloeden & C Schinas (eds), Differential and Difference Equations with Applications, ICDDEA 2019. vol. 333, Springer Proceedings in Mathematics and Statistics, vol. 333, Springer Nature Switzerland, Cham, pp. 225-237. https://doi.org/10.1007/978-3-030-56323-3_18

Dynamical Models of Interrelation in a Class of Artificial Networks. / Sadyrbaev, Felix; Atslēga, Svetlana; Brokan, Eduard.
Differential and Difference Equations with Applications, ICDDEA 2019. ed. / Sandra Pinelas; Sandra Pinelas; John R. Graef; Stefan Hilger; Peter Kloeden; Christos Schinas. Vol. 333 Cham: Springer Nature Switzerland, 2020. p. 225-237 (Springer Proceedings in Mathematics and Statistics; Vol. 333).

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › Research › peer-review

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N2 - The system of ordinary differential equations that models a type of artificial networks is considered. The system consists of a sigmoidal function that depends on linear combinations of the arguments minus the linear part. The linear combinations of the arguments are described by the regulatory matrix W. For the three-dimensional cases, several types of matrices W are considered and the behavior of solutions of the system is analyzed. The attractive sets are constructed for most cases. The illustrative examples are provided. The list of references consists of 12 items.

AB - The system of ordinary differential equations that models a type of artificial networks is considered. The system consists of a sigmoidal function that depends on linear combinations of the arguments minus the linear part. The linear combinations of the arguments are described by the regulatory matrix W. For the three-dimensional cases, several types of matrices W are considered and the behavior of solutions of the system is analyzed. The attractive sets are constructed for most cases. The illustrative examples are provided. The list of references consists of 12 items.

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KW - Attractors

KW - Critical points

KW - Dynamical systems

KW - Gene regulatory networks

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Sadyrbaev F, Atslēga S, Brokan E. Dynamical Models of Interrelation in a Class of Artificial Networks. In Pinelas S, Pinelas S, Graef JR, Hilger S, Kloeden P, Schinas C, editors, Differential and Difference Equations with Applications, ICDDEA 2019. Vol. 333. Cham: Springer Nature Switzerland. 2020. p. 225-237. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-030-56323-3_18

Dynamical Models of Interrelation in a Class of Artificial Networks

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